{ "cells": [ { "cell_type": "markdown", "id": "22f94a3b", "metadata": {}, "source": [ "# [Non-Abundant Sums](https://projecteuler.net/problem=23)\n", "\n", "Just like in [problem 21](https://projecteuler.net/problem=21), we'll define an `aliquot_sum` function and use that to find all the [abundant numbers](https://en.wikipedia.org/wiki/Abundant_number) below 28,124. Then we check every integer less than 28,124 to see if it's the sum of any two abundant numbers, and if it is, remove it from a set containing all those integers. Whatever's left in that set are the non-abundant sums." ] }, { "cell_type": "code", "execution_count": 1, "id": "6747d2a3", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "4179871\n" ] } ], "source": [ "aliquot_sum = lambda n: sigma(n) - n\n", "\n", "abundant_numbers = {k for k in range(1, 28124) if aliquot_sum(k) > k}\n", "\n", "non_abundant_sums = set(range(1, 28124))\n", "for n in range(1, 28124):\n", " for m in abundant_numbers:\n", " if n - m in abundant_numbers:\n", " non_abundant_sums.discard(n)\n", " break\n", "\n", "print(sum(non_abundant_sums))" ] }, { "cell_type": "markdown", "id": "91a43bd1", "metadata": {}, "source": [ "## Relevant sequences\n", "* Numbers that are not the sum of two abundant numbers: [A048242](https://oeis.org/A048242)" ] } ], "metadata": { "kernelspec": { "display_name": "SageMath 9.5", "language": "sage", "name": "sagemath" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.11.2" } }, "nbformat": 4, "nbformat_minor": 5 }